Description:

Topics in algebraic stacks and how it relates to K-stability and other moduli notions. We plan to focus on topics including, but not limited to, foliations, algebraic stacks, K-stability and K-moduli, moduli theories and birational geometry. We plan for this seminar to be a supplement to the usual weekly algebraic geometry seminar, covering a broad range of topics in moduli theories which have been prevalent in wide areas of modern algebraic geometry.

Oct. 22, 2025

Speaker: Iacopo Brivio

Affiliation: Center for Mathematical Sciences and Applications (CMSA), Harvard University

Title: Antiitaka conjecture for fibrations in positive characteristic.

Abstract: A famous conjecture by Iitaka predicts that, given a fibration $f\colon X\to Y$ of smooth complex varieties with general fiber $F$, then the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$ holds. It was recently shown by Chang that, when the stable base locus $\mathbb{B}(-K_X)$ is $f$-vertical, then a similar inequality holds for the anticanonical divisor: $\kappa(-K_X)\leq \kappa(-K_F)+\kappa(-K_Y)$. Over fields of positive characteristic it is known that both Iitaka's conjecture and Chang's theorem can fail. However the expectation is that, when $F$ is sufficiently well-behaved with respect to the Frobenius morphism, then these results should hold. In this talk I will show that this is the case for Chang's theorem. This is based on joint work with Benozzo and Chang.